NGSolve Examples

In this example we will have a look on how we can solve a multiphysics problem in NGSolve and the NGSPy interface. Therefore, we will consider a fluid-structure interaction problem, where the Navier-Stokes equations for the fluid part

$$\rho \frac{\partial u}{\partial t}+\rho (u\cdot \mathrm{\nabla })u-\rho \nu \mathrm{\Delta }u+\mathrm{\nabla }p=f$$ $$\text{div}(u)=0$$

and the elastic wave equation for the elastic part

As this may be useful for some people I decided to write a short article about how one can do distributed parameter tests either on a cloud or on a cluster. As a test case, we will solve the poisson equation for some 1000 different conductivities - automatically distributed onto all available computing nodes. Apart from NGSolve we will use dispy to manage the network communication.

The newly introduced BBND feature of Netgen/NGSolve allows us to compute the magnetic field of a thin wire by approximating it with operators on the 1D line segment. In this example we want to compute the field of the following coil geometry:

In this example we want to show how one can easily implement an error estimator for the Poisson problem $-\mathrm{\Delta }u=f$ given by $$\eta (u_h{)}^2:=\sum _{T\in \mathcal{T}}{h}_T^2\Vert f+\mathrm{\Delta }{u}_h{\Vert }_{L^2(T)}^2+\sum _{E\in \mathcal{F}}{h}_E\Vert [[\mathrm{\nabla }{u}_h\cdot n]]{\Vert }_{L^2(E)}^2.$$

Sometimes it is convenient to export results that were obtained with NGSolve to third party visualization tools (for rendering/videos etc.). A simple way to do this is the export to the VTK format (ascii) that is provided from NGS-py.